Was quick to get an account into the red (5)

I believe the answer is:
raced
'was quick to get' is the definition.
I can't judge whether this defines the answer.
'account into the red' is the wordplay.
'account' becomes 'ac' (abbreviation for account).
'into' indicates putting letters inside.
'ac' put inside 'red' is 'RACED'.
'an' acts as a link.
Can you help me to learn more?
(Other definitions for raced that I've seen before include "Went fast" , "Went quickly round" , "Ran competitively" , "Competed" , "Ran fast" .)